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61.
We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T
1, the population relaxation rate, and 1/T
2, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T
21/2T
1, when fourth-order terms are included, in some instances 1/T
2<1/2T
1. 相似文献
62.
It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy. 相似文献
63.
Nonlinear systems with stochastic parameters are approximated by simpler systems using a method that we call statistical replacement. This method is an extension of the previously developed AGREE which was restricted to systems with additive fluctuations. Statistical replacement incorporates the distinctions between globally stable thermodynamically closed systems and thermodynamically open systems that can be unstable. 相似文献
64.
65.
R. Centoducatte E. P. Muniz F. E. Jorge M. T. Barreto 《Journal of Molecular Structure》2004,680(1-3):143-147
The molecular improved generator coordinate Hartree–Fock (MIGCHF) method is used to generate accurate basis sets of primitive Gaussian-type functions for the H2O molecule. Sequences of increasing size atom centered basis sets are employed to explore the accuracy that can be achieved with this method. Using the O(24s14p8d5f2g1h);H(22s9p5d2f1g) basis set, the HF and second-order electron correlation energies of the H2O ground state at the experimental geometry are computed as −76.0674680 and −0.3491935 hartree, respectively. The HF energy is in error by 20 μhartree and the second-order correlation energy corresponds to 96.5% of an estimate of the limiting value. The relevance of the present calculations is to show the accuracy that can be achieved in studies of small polyatomic molecules with the MIGCHF method. 相似文献
66.
A discrete variable representation (DVR) made from distributed Gaussians gn(x) = e, (n = ?∞, …, ∞) and its infinite grid limit is described. The infinite grid limit of the distributed Gaussian DVR (DGDVR) reduces to the sinc function DVR of Colbert and Miller in the limit c → 0. The numerical performance of both finite and infinite grid DGDVRs and the sinc function DVR is compared. If a small number of quadrature points are taken, the finite grid DGDVR performs much better than both infinite grid DGDVR and sinc function DVR. The infinite grid DVRs lose accuracy due to the truncation error. In contrast, the sinc function DVR is found to be superior to both finite and infinite grid DGDVRs if enough grid points are taken to eliminate the truncation error. In particular, the accuracy of DGDVRs does not get better than some limit when the distance between Gaussians d goes to zero with fixed c, whereas the accuracy of the sinc function DVR improves very quickly as d becomes smaller, and the results are exact in the limit d → 0. An analysis of the performance of distributed basis functions to represent a given function is presented in a recent publication. With this analysis, we explain why the sinc function DVR performs better than the infinite grid DGDVR. The analysis also traces the inability of Gaussians to yield exact results in the limit d → 0 to the incompleteness of this basis in this limit. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 相似文献
67.
Daniel M. Chipman 《Theoretical chemistry accounts》1989,76(2):73-84
Summary The suitability of Gaussian basis sets for ab initio calculation of Fermi contact spin densities is established by application to the prototype first-row atoms B-F having open shell p electrons. Small multiconfiguration self-consistent-field wave functions are used to describe relevant spin and orbital polarization effects. Basis sets are evaluated by comparing the results to highly precise numerical grid calculations previously carried out with the same wave function models. It is found that modest contracted Gaussian basis sets developed primarily for Hartree-Fock calculations can give semiquantitative results if augmented by diffuse functions and if further uncontracted in the outer core-inner valence region. 相似文献
68.
In this article, we apply a novel time‐dependent discrete variable representation (TDDVR) method proposed by Barkakaty and Adhikari to investigate tunneling through an Eckart barrier. This semi‐classical method is theoretically rigorous and straightforward to implement. Among the TDDVR formulations, this report presents the first derivation of a rigorous form of quantum force (QF) for the present perspective. The validity of this semi‐classical approach is demanded based on the excellent agreement of the tunneling probability with the corresponding quantum results. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004 相似文献
69.
J. Hyslop 《Theoretical chemistry accounts》1973,31(3):189-194
An account is given of the use of Gaussian quadrature product formulae in the evaluation of certain six-dimensional, two-centre integrals involving one-electron Green's functions. These integrals occur in a new molecular variational principle recently proposed by Hall, Hyslop and Rees [1] from which an approximate energy may be derived which can be shown to be at least as good as that obtained from the Rayleigh-Ritz principle. Reductions in computing time are realized by removing certain singularities using a subtraction technique and also by using an empirically determined Richardson-type extrapolation formula.This paper was presented during the session on numerical integration methods for molecules of the 1970 Quantum Theory Conference in Nottingham. It has been revised in the light of the interesting discussion which followed. 相似文献
70.
Yong WANG 《数学年刊B辑(英文版)》2022,43(3):443-458
In this paper, the author computes canonical connections and KobayashiNomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. He defines algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. He classifies algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure. 相似文献